title: Ribbon crystals.
abstract: A repetitive crystal-like pattern is spontaneously formed upon the twisting of straight ribbons. The pattern is akin to a tessellation with isosceles triangles, and it can easily be demonstrated with ribbons cut from an overhead transparency. We give a general description of developable ribbons using a ruled procedure where ribbons are uniquely described by two generating functions. This construction defines a differentiable frame, the ribbon frame, which does not have singular points, whereby we avoid the shortcomings of the Frenet-Serret frame. The observed spontaneous pattern is modeled using planar triangles and cylindrical arcs, and the ribbon structure is shown to arise from a maximization of the end-to-end length of the ribbon, i.e. from an optimal use of ribbon length. The phenomenon is discussed in the perspectives of incompatible intrinsic geometries and of the emergence of long-range order.
authors.affiliation: Department of Micro and Nanotechnology, Technical University of Denmark, Kongens Lyngby, Denmark.
authors.forename: Jakob
authors.initials: J
authors.lastname: Bohr
authors.forename: Steen
authors.initials: S
authors.lastname: Markvorsen
mesh_terms: D004247:DNA / Q000737:chemistry; D055595:Mechanical Phenomena; D008958:Models, Molecular; D009690:Nucleic Acid Conformation; D013499:Surface Properties
chemical_list: D004247:DNA